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An Algebraic Approach to Convolutions and Transform Methods

✍ Scribed by Luis Verde-Star

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
255 KB
Volume
19
Category
Article
ISSN
0196-8858

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✦ Synopsis

We show that the Hopf algebra dual of the polynomials in one variable appears often in analysis, but under different disguises that include proper rational functions, exponential polynomials, shift invariant operators, Taylor functionals, and linearly recurrent sequences. The isomorphisms from the proper rational functions to the other algebras yield an explicit and general method for the solution of linear functional equations, which can be considered as an algebraic version of the usual integral transform methods. We also explain how some of the usual convolution products in spaces of functions arise in an algebraic way.

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